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AIAA 2000-0757 

Wake Vortex Transport and Decay in Ground 
Effect: Vortex Linking with tlie Ground 

Fred H. Proctor and David W. Hamilton 
NASA Langley Research Center 
Hampton, VA 

Jongil Han 

North Carolina State University 

Raleigh, NC 




38th Aerospace 

Meeting & Exhibit 

January 10-13, 2000/ Reno, NV 



For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 
1801 Alexander Bell Drive, Suite 500, Reston, Virginia 20191-4344 



AIAA-2000-0757 

Wake Vortex Transport and Decay in Ground Effect: Vortex Linking 

with the Ground 



Fred H. Proctor* and David W. Hamilton* 
NASA Langley Research Center 
Hampton, Virginia 

Jongil Han* 

North Carolina State University 

Raleigh, NC 



Abstract 

Numerical simulations are carried out with a three- 
dimensional Large-Eddy Simulation (LES) model to 
explore the sensitivity of vortex decay and transport in 
ground ejfecl (IGE). The vortex decay rates are found to 
be strongly enhanced following maximum descent into 
ground effect. The nondimensional decay rate is found to 
be insensitive to the initial values of circulation, height, 
and vortex separation. The information gained from 
these simulations is used to construct a simple decay 
relationship. This relationship compares well with 
obser\'ed data from an IGE rase study. Similarly, a 
relationship for lateral drift due to ground effect is 
constructed from the LES data. In the second part of this 
paper, vortex linking with the ground is investigated. Our 
numerical simulations of wake vortices for IGE show that 
a vortex may link with its image beneath the ground, if the 
intensity of the ambient turbulence is moderate to high. 
This linking with the ground (which is ob.ferved in real 
cases) gives the appearance of a vortex tube that bends to 



*Research Scientist, Airborne Systems Competency, 
AlAA member 

^Research Scientist, Airborne Systems Competency 
Research Scientist, Department of Marine, Earth, and 
Atmospheric Sciences, AIAA member 



Copyright © 2000 by the American Institute of 
Aeronautics and Astronautics, Inc. No copyright is 
asserted in the United States under Title 17, U.S. Code. 
The Government has a royalty-free license to exercise 
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Government purposes. All other rights are reserved by 
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become vertically oriented and which terminates at the 
ground. From the simulations conducted, the linking time 
for IGE appears to be similar to the linking time for 
vortices in the free atmosphere: i.e.. a function of ambient 
turbidence intensity. 



B 

b„ 

H 

Lx,Ly 

M 

r 
r, 
t 

T 
Tr, 

Va 

v„ 

X 

y 
Y 



•-mm 

z, 
r 
r„ 
p 

e 



Nomenclature 
aircraft wing span 
initial vortex separation - k B/4 
acceleration due to gravity 
domain length in x and y directions, respectively 
domain depth 
mass of generating aircraft 
radius from vortex center 
radius of peak tangential velocity 
time coordinate 
nondimensional time - / V„/b„ 

I at Z = Zmin 

airspeed of generating aircraft 

initial vortex descent velocity - VJ (2 n b„) 

horizontal coordinate along flight path 

horizontal coordinate lateral to fight path 

nondimensional lateral coordinate - y/b„ 

vertical coordinate 

minimum altitude achieved during vortex descent 

initial height above ground of wake vortex 

vortex circulation 

initial vortex circulation - M gl(b„p V^) 

air density 

ambient turbulence (eddy) dissipation rate 

AT-component of vorticity 

kinematic viscosity 

nondimensional eddy dissipation - (e b„) V„ 



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I. Introduction 

Aircraft wake vortices are formed when vorticity 
generated by lift rolls up into two primary trailing 
vortices. The two vortices have a characteristic initial 
separation, b„, which is proportional to the wingspan of 
the generating aircraft. The wake vortices are considered 
to be "in ground effect" (IGE) when located within one 
initial separation of the ground (i.e.. ; < b„). ' The 
prediction for the location and intensity of these vortices 
is important for systems that are to manage safe aircraft 
spacings. 

The complex influence of the ground on wake vortex 
behavior has been the focus of numerous investigations, 
including the observations by Harvey and Perry," 
Hallock,' Kopp,* Hallock and Bumham,' Burhnam and 
Hallock," and Rudis el al.^ as well as the numerical 
studies by Schiling,' Robins and Delisi,' Zheng and Ash,'° 
Corjon and Poinsot," Corjon and Stoessel,'" and Proctor 
and Han." Qualitative understanding of basic vortex 
transport mechanisms for IGE is known, but quantitative 
relationships are needed. Wake vortex decay is known to 
be enhanced by proximity to the ground, but much is to be 
learned about this behavior.'' 

Three-dimensional instability of wake vortices near 
the ground is largely unexplored. Lateral linking of the 
vortex pair associated with Crow instability''' should be 
less likely due to the increased separation forced by the 
ground's presence. Ground linking -- the linking of a 
vortex with its image vortex beneath the ground plane - 
has been observed," but thought to be rare,"' Linking 
instabilities can increase the uncertainty of a vortex's 
position and may affect the vortex decay rate as well. 

Semi-empirical vortex prediction algorithms have 
been developed by Robins et al. ' that include the ground's 
influence on lateral separation and vortex rebound. 
Similar algorithms" have been incorporated within 
NASA's Aircraft VOrtex Spacing System(AVOSS)." "™ 
Improved accuracy of these prediction algorithms depend 
on the better understanding of vortex transport and decay 
near the ground. Numerical experiments with a Large 
Eddy Simulation (LES) model are being conducted in 
order to provide guidance for the enhancement of these 
prediction algorithms."' 

This paper is a continuation of the three-dimensional 
LES study described in Proctor and Han," with further 
focus on vortex decay within IGE. In Proctor and Han, 
we investigated the sensitivity over a wide range of 
ambient turbulence levels of a wake vortex for a landing 
L-IOIl that was observed on 26 September 1997 at 
Dallas-Fort Worth (DFW) airport." The simulations 



showed only a weak sensitivity to the level of ambient 
turbulence, and were in very-good agreement with Lidar- 
derived observations. The results indicated that enhanced 
decay from ground effect begins a few seconds after the 
vortices descend to their minimum height, with vortex 
decay prior to these times being primarily influenced by 
stratification and ambient turbulence. The study also 
found that vertical oscillations associated with vortex 
rebound were less prominent for higher levels of ambient 
turbulence, since the secondary vortices were more likely 
to be diminished by the stronger turbulence. Also 
addressed was the influence of ground stress on wake 
vortex transport. The study determined that viscous 
stress reduced the velocity near the ground and acted to 
decouple the primary vortices from their sub-ground 
images. If ground stress was ignored, unrealistic 
divergence of the vortex pairs ensued. The study, did not 
address Crow instability, or similar linking instabilities. 



Table L Salient Characteristics of TASS 



Primitive equation / non-Boussinesq equation set Time- 
dependent, nonhydrostatic, compressible. 

Meteonoiogical framework with option for either three- 
dimensional or two-dimensional simulations. 

Large Eddy Simulation nxxJei with ist-order subgtid 
scale turbulence ckjsure - Grid-scale turbulerxse 
explicitly computed, while effects of subgrid-scale 
turtxilence modeled by Smagorinsky model with 
modifications for stratircation and flow rotation. 

Ground stress based on Monin-Obukhov Similartty 
theory. 

Optional boundary conditions - open conditions utilizes 
mass-conservative, nonreflective radiation boundary 
scheme. 

Explicit nunnerical schemes, quadratic consen/ative, 
time-split compressible-- accurate as well as Nghly 
efficient, and essentially free of numerical diffusion. 
Space derivatives computed on Arakawa C-grid 
staggered mesh with 4'''-orcler accuracy for oonvectwe 
terms. 

Prognostic equatk>ns for vapor and atmospheric water 
sut>stance (e.g. doud droplets, rain, snow, hail, ice 
crystals). Large set of microphysical-parameterization 
models. 

Model applicable to meso^and microscale atmospheric 
phenomenon. Initialization modules for simulation of 
convective storms, microbursts, atmospheric boundary 
layers, turtjulence, and aircraft wake vortices. 



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since the assumed domain had a limited axial depth. In 
the present paper, we address the sensitivity of vortex 
decay for IGE, by conducting LES of wake vortices with 
different initial heights, separations and circulations. The 
results are normalized and a simple analytical 
representation for IGE decay is given. Similarly, a simple 
model based on the LES results is proposed for lateral 
drift due to ground effect. In the second part of this paper, 
we examine the occurrence of ground linking and its 
sensitivity to ambient turbulence. 

II. The Model and Initial Conditions 

The numerical model used in this study is a three- 
dimensional LES model called the Terminal Area 
Simulation System*' (TASS), which has been adapted for 
simulation of wake vortex interaction with the 
atmosphere.'^'' The numerical model used in this study 
differs from that in many previous investigations, in that: 
I ) time-dependent computations are carried out in three- 
dimensional space, 2) the formulation is essentially free of 
numerical diffusion,"' 3) the computations are LES and at 
high Reynolds number, 4) the experiments are initialized 
with realistic turbulence fields, and 5) realistic surface- 
stress and subgrid turbulence-closure formulations are 
assumed. Salient characteristics of TASS are listed in 
table 1. 

Model Equations 

The TASS model contains a prognostic equation set 
for momentum, temperature and pressure, and employs a 
compressible time-split formulation. Omitting nx)isture and 
coriolis terms (which are not used in these simulations), the 
TASS equation set in standard tensor notation is as follows: 



Thermodynamic Equation (Potential Temperature): 

de__ I d9p„Hj e ^p„uj 

p„dxj Oxj 



with the Potential Temperature defined as: 

In the above equations, u, is the tensor component of 
velocity, ( is time,;; is deviation from atmospheric pressure 
P,r is atmospheric temperature, p is the air density, Cp and 
Cv are the specific heats of air at constant pressure and 
volume, n is the earth's gravitational acceleration, R,i is the 
gas constant for dry air, P„„ is a constant equivalent to 1 000 
millibars (lO' pascals) of pressure. Environmental state 
variables, e.g., Po , Po and 0,, . are defined from the initial 
input sounding and are functions of height only. 

A modi fied Smagorinsky first-order closure is used for 
the subgrid eddy viscosity as: 



dx, 



r d 



Xk 



'^4'-°^lJ<is-ct2Rir 



The subgrid eddy viscosity for momentum, K^, is modified 
by the Richardson numbers, for stratification, /fi,, and for 
flow rotation, Ri,. with a, =3 and 02= 1 .5. 



Momentum: 
du, ^ H dp 
9' Pn'dxi 



Or, d.i 



'Xj 



^-^P„KMl^^f^-=--^5,jl 
dxi Ox, 3 dx. 



Pj 



Xj 



Buovamy Term: 



tXj 



'Xj 

duj 2 ^"k 
dxt 



H = l 



e PC. 



do Po C p 

Pressure Deviation: 
dp C pP Ouj _ 
dt Cv ^Xj 



I 



PoSUjSj} 



The subgrid length scale. Is , is determined from the 
grid volume and is matched to the appropriate length scale 
close to the ground where the flow is under-resolved. That 
is: 

oA z>oA/k 



aA[I + (aA/kzr'] 



l + faA/kzf" 
kz 



aA/k>z>Az/2 

z<Az/2 



where k is von Karman's constant, and where m and a are 
invariant constants with values defined as m = 3 and a = 
0.15. The filter width is based on the minimal resolvable 
scale; 

A=/2A.v2Ay2Ac /'■'■' 



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where At, dy. and A: arc the numerical grid sizes in the 
respective x, y, ;: direction. 

The ground boundary is impermeable with nonslip 
velocity specifications. The surface stress due to the 
ground is determined locally from the wind speed, surface 
roughness, and the local thermal stratification. Details of 
the surface formulation are in the appendix of reference 
[13]. 

Turbulence Initialization 

Prior to vortex initialization, an initial field of 
resolved-scale turbulence is allowed to develop under an 
artificial external forcing at low wavenumbers." The 
approach is similar to that in recent studies with TASS, 
where wake vortex decay and the development of Crow 
instability is examined within a Kolmogorov*^ spectrum 
of homogeneous turbulence (Han et al.' ' ). The method, 
however, is slightly different for the present study, due to 
the inclusion of the ground. Since periodic boundary 
conditions are assumed only at the horizontal boundaries, 
the turbulence forcing is applied only to horizontal 
velocity over each horizontal plane. Nevertheless, the 
influence of the horizontal two-dimensional forcing 
spreads quickly to the vertical direction as well as to the 
vertical velocity through the mass continuity. 




Figure 1 . Turbulence energy spectrum atz=I4 m before 
vortex injection. Here, subscripts 2 and 3 denote 
crossflow and vertical directions, respectively. 

Because the TASS code uses a finite difference 
numerical scheme, the forcing is achieved by performing, 
first, a two-dimensional fast Fourier transform (FFT) at 
every large time step, then adding a constant amplitude to 
all the modes with integer wavenumbers whose magnitude 



is less than 3.0. and finally, performing an inverse FFT 
back to the physical space. At the same time, the 
horizontal domain average temperature and velocity fields 
are forced to maintain their initial vertical profiles by 
subtracting the difference every time step. Due to subgrid 
dissipation, the simulation can reach a statistically steady 
state, in the sense that the mean turbulence kinetic energy 
oscillates in time around a constant value. 

Figure 1 shows a one-dimensional energy spectrum 
with a -5/3 slope of Kolmogorov's"' spectrum when the 
turbulent flow field has achieved a statistically steady 
state. Figure 1 indicates that our approach can produce a 
well-developed turbulent flow field that possesses 
Kolmogorov's inertial subrange. The eddy dissipation rate 
£ is estimated from the well-known technique of fitting 
Kolmogorov's theoretical spectrum in the inertial 
subrange to the simulated spectra. 

Vortex Initialization 

The initial wake vortex field is specified with a 
simple vortex system that is representative of the post roll- 
up, wake-vortex velocity field. The vortex system is 
initialized with the superposition of two counter-rotating 
vortices that have no initial variation in the axial direction. 
The tangential velocity, V, associated with each vortex, is 
determined from: 



V(r} = 



2nr 



1-Expl-I0\- 



where, r is the radius from the center of the vortex. V^ 
the circulation at r >> r^, and B is the span of the 
generating aircraft. The above formula is based on Lidar 
observations of wake vortices measured early in their 
evolution. The model is applied only at r > r,. and is 
matched with a Lamb model profile for r < r^. The 
values assumed for initial vortex separation and 
circulation are derived from an aircraft's weight, span, 
and airspeed according to conventional formula based on 
elliptical loading; i.e., i„ = 7tB/4, and T., = 4W^/(7lBpV„). 
Appropriate vortex image conditions are applied to the 
initial wake field to ensure consistency and mass 
continuity at the TASS model boundaries. 

Except when otherwise noted, the initial vortex 
parameters (table 2) are taken from the observed aircraft 
parameters for the L-IOI I, as was used in Proctor and 
Han." 

All simulations are conducted with dimensional 
variables and assume turbulent flow with a rotational 
Reynolds number (F./v) of -10 . 



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Table 2. Inilial vortex parameters (baseline). 



Parameter 

Vortex spacing (fe„) 
Generating height (Zi) 
Vortex circulation (P,,) 
Vortex core radius 



Value 



37 m 

16 m (0.432 fc„) 

390 m's' 

3 m (fc„/12.3) 



Model Domain Parameters 

Two domain sizes are used for the experiments in 
this paper. A short domain, which has been truncated in 
the A^-direction (L,. Ly, L. = 81 m. 370 m, 81 ni). and a 
long domain (L^, Ly, L. = 451 m, 337 m, 81 m). For an 
assumed initial vortex separation of b„=37 m, this would 
translate into: (2.2x 10x2.2) b„ for the short domain and 
02.2x9.1 X 2.2) b„ for the long domain. Bothlongand 
short domains are resolved by the grid sizes listed in table 
3. 



Table 3. Grid Resolution. 



Parameter Value 

Vertical resolution (Az) ' -5 m 

Lateral resolution (Ay) 1 .5 m 

Axial resolution (Ax) 2.0 m 



The advantage of the short domain is that it allows 
economical calculations of vortex behavior and simplifies 
the analysis of results. The longer domain, however, is 
less likely to hinder three-dimensional linking instabilities. 
A comparison of results from the two domain sizes is 
shown in the appendix. 

Determination of Vortex Position and Circulation 

Based on the vortex position in each crossflow plain, 
circulation is computed for each crossflow plane according 
to: 
rr(-v) = JjX, dydz 

The circulation is not computed for any plane where the 
vorticity vector is beyond 30" of the .v-axis. 

A 5-15 meter averaged-circulation, is computed 
according to: 

where a=5 m, and b = 15 m. The 5-15 m average 
circulation is chosen to characterize the intensity of the 
vortex, since it quantifies the hazard faced by an 
encountering aircraft™" 



A mean average circulation is reported for each time 
interval by computing a mean of the circulations from each 
crossflow plane: 



t; "■"- 



N' 



Similarly, a mean vortex position is reported for each 
time interval by averaging the positions from each 
crossflow plane. 

III. IGE Sensitivity 

Three sets of experiments are conducted in order to 
determine the sensitivity of vortex decay within ICE. The 
short domain is assumed which will inhibit the occurrence 
of linking instabilities. All of the simulations assume 
neutral stratification, no mean ambient winds, and an 
ambient turbulence dissipation rate of e =9.6 x 10 ' m' 
.V '. Other initial conditions for the simulations are listed 
in tables 2 and 3. 

Sensitivity to Initialization Height 

Five experiments are conducted for a vortex 
initialization height (Z,) of: 0.32 b„. 0.5 b„. 0.65 b,.. 0.84 
fc,„ and 1.0 b„. Comparisons of the experiments are shown 
in Fig. 2 as function of nondimensional time. Note that 
the lime coordinate for each experiment is offset by the 
time of maximum descent into ground effect; i.e., by 
T,;=T(zmin). The curves for normalized 5-15 m average 
circulation, as well as the normalized lateral positions tend 
to collapse, once the offset time T,-, is accounted for. As 
also shown in our previous study," vortex decay is 
significantly enhanced following maximum penetration 
into ICE. In addition, these results show the decay rate to 
be more or less independent of the vortex inilial height, 
with the enhanced level of decay beginning roughly 0.25 
nondimensional time units following Tn 

A formula for the decay of average circulation can 
be obtained from these results as 

_r 
r, 



= Expl- 



■2f/--7-„„r 



(1) 



where T„„ = T,-, +0.25 (i.e., 0.25 nondimensional time 
units following the time of maximum penetration into 
ground effect), and r„„ is the circulation at 
nondimensional time T,„. The above formula is 
independent of ambient turbulence and can only be 
applied for T > T,-, +0.25. 

Differentiating the above gives the rate of decay as: 



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dr 

, dT 



l^iT-T^i 



-Expi 



-2(T -T ) 

^1 ' ' no f 



2/i 



A plot of the curve from Eq. I is shown also in Fig. 
2c and agrees very well with the LES results. 

An empirical relationship for lateral spread within 
IGE can be determined from the LES results as well. The 
vortices, which start at a lateral distance from the flight 
path of y = ± '/ib„. diverge lateral with time due to the 
influence of the ground. Figure 2b indicates (in the 
absence of crosswind) that the vortices asymptote toward 
v = 2b„; approaching a maximum separation of about 4b„. 
Based on these results, an empirical relationship for 
vortex drift due to ground effect is: 



Y=I.385(T-T,:) 



,0.227 



for T>T,: + 0.25 (2) 



where Y is the normalized lateral position from the flight 
path. The vortex separation, b = 2Yb„, also can be 
predicted for IGE with Eq. 2. A plot of the curve from 
£17. 2 is compared with LES data in Fig. 2b. 

The lateral drift rate can be determined by 
differentiating (2) giving: 

Vc = — = 0.3I73( T-Tq f°''" for T > To + 0.25 
dT 

where V,-, is the nondimensional velocity for lateral drift 
due to ground effect (this velocity can be made 
dimensional by multiplying by the initial vortex sink rate, 
V„). 

Sensitivity to Initial Vortex Spacing 

In order to further evaluate the sensitivity of our 
results and test the validity of Eq. 1, three additional 
experiments are conducted, which assume different initial 
vortex spacings (b„) as listed in table 4. An initial 
circulation of 400 mV and an initial height of Z,= 0.432 
b„ is assumed for each experiment. Values for Z, and 
nondimensional turbulence dissipation are slightly 
different in these experiments due to the variation in b„. 

Table 4. Initial vortex .separation (bj and corresponding 
initial altitude (Z,) and dimensionless turbulence intensity 
(r\) for .sen.silivir\i to initial vortex sparing cases. 



b„(m) 

30 
37 
49 



Z|(m) 



.Jl 



13 
16 

21.2 



0.0671 
0.0897 
0.1291 



IGE Sensitivity Test for Varying Vortex Heights ( n=0.091 ) 
Vortex Vertical Position History (Port) 

(A) 



1 

0.9 

0.8 

20,7 

S06 

f 0.5 

I 0.4 

0.3 

0.2 

0.1 







, _^ " 
















t J*^ ^^-*- — ' 




\ j^ ^r* ,' .-■ 


- 


A y^ ^*~^ •''" 


- 


\ j^y 




"V /y^ 




\^'y ...-■ •■ 


" 


K-'/y 














- 


?.05Ob; 




^.065b. 




^ = 84b. 


- 


^ = 1 00 b„ 


i 1 


, , 1 , 1 , , , , 1 , 1 , , , 1 



12 3 

Nondimensional Time (T - T„) 



IGE Sensitivity Test for Varying Vortex Heights ( ii=0 091 ) 
Vortex Lateral Position History (Port) 




12 3 

Nondlmensionai Time (T - TJ 



IGE Sensitivity Test for Varying Vortex Heights (r|=0.091 ) 
Vortex 5-15 m Averaged Circulation History (Port) 



(C) 



^a0 32b„ 

^ = 050b, 

_. ^ = 065b„ 

Z. = 0&ib^ 

^ =. 1 00 b„ 

MM^^^ 0«caY Model 




12 3 4 

Nondlmensionai Time (T - T^) 



Figure 2. Sensitivity to vortex initiation height. 
Nondimensional height (a), nondimensional lateral 
position (b). and nondimensional 5-15 m average 
circulation (c) v.v nondimensional lime. "Decay model " in 
(C)from Eq.l and "Cun'e fit" in (B)from Eq.2. 



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IGE Sensitivity Test for Varying Initial Separation {b„) 
Vortex Vertical Position History { Zi=0.43b„) 




b, > so m, n > 0.0671 

.» _ * bo - 37 m, T^ > 0.08S7 
— ~— .» b, > 49 m, T^ « 0.1291 



12 3 4 

NondlmenslonalTlme (t b^J 



IGE 



Sensitivity Test for Varying Initial Separation (b„) 
Vortex Lateral Position History ( Zi=0.43b„) 




12 3 4 

Nondlmenslonal Time (t b^„) 



IGE Sensitivity Test for Varying Initial Separation (b^) 
Vortex 5-15 m Average Circulation History ( Zi=0.43bj) 



1.2 


r 


(C) 


1 
0,8 


^ 


b, • JO m, n " 0.0971 

b, > 37 m, n « 0.0887 


0.6 


^ 


V^ 


0.4 


- 


^**^^ 


0.2 


, : , . 1 


I, II 1 



12 3 4 

Nondlmenstonal Time (t b^ J 



Figure 3. Same as Fig. 2, but for sensitivity to initial 
vortex spacing. 



IGE Sensitivity Test for Varying Initial Circulation 
Vortex Vertical Position History 

(A) 




12 3 4 

Nondimenskmal Time (t b^V J 



IGE Sensitivity Test for Varying Initial Circulation 
Vortex Lateral Position History 

(B) 




12 3 4 

Nondlmenslonal Time (t b^ J 



IGE Sensitivity Test for Varying Initial Circulation 
Vortex 5-15 m Average Circulation History 

(C) 
1 2r 



« 250 mV.,1« 0.1420 

— — - [ , « 300 m'/s, n > 0.1 183 

. I '.350 m'/s.r|> 0.1014 

r^ > 400 mVs, n > 0.0887 

r^ > 450 mV*. n - 0.0789 

^^^^^m Dacay Mod«l 




12 3 4 

Nondlmenslonal Time (t b^VJ 



Figure 4. Same as Fig. 2. but for sensitivity to initial 
vortex circulation. 



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The results presented in Fig. 3 show that the curves 
again collapse to a similar value when normalized, and 
that the proposed formulas for IGE decay and lateral drift 
are in excellent agreement with the LES results. 
Enhanced levels of decay due to IGE begin at T=0.5 
(which is Tc,+0.25) for all three cases. 

Sensitivity to Initial Circulation 

In the third set of experiments, five simulations with 
different initial circulations are conducted (table 5). All 
else is assumed equal, with Tl being different due to its 
dependency on r„. 



intensity, or specifically, the eddy dissipation rate -*" " 
The goal of the experiments in this section is to examine 
ground linking and any sensitivity that it may have to the 
level of ambient turbulence. All of the experiments 
assume the long domain so as to permit linking 
instabilities. The experiments also assume the parameters 
listed in tables 2 and 3, as well as the initial sounding in 
Fig. 5. The nondimensional turbulence strengths, Tl, used 
in these experiments, range from 0.2.?.? to 0.75. These 
values represent a typical range between moderate to very 
turbulent atmospheric boundary layers. 



Again, the curves collapse with a tight spread (Fig. 
4), and the proposed IGE decay and drift formulas are in 
excellent agreement with LES results. 



Table 5. Initial circulation (FJ and corresponding 
dimensionless turbulence intensity for F^semitivity cases. 



250 
300 
350 
400 
450 



n 

0.1420 
O.I 183 
0.1014 
0.0887 
0.0789 



IV. Comparison with Observed Case. 

In this section, the new formula for IGE decay 
(Eq. I) is compared with the LES simulation for a landing 
L-IOII, which was observed at 20.09 UTC on 26 
September 1997 at Dallas-Fort Worth (DFW) airport. 
The input sounding for temperature and crosswind is 
shown in Fig. 5. The simulation is conducted with the 
short domain and with the parameters listed in tables 2 
and 3. The simulation includes an ambient turbulence 
field with, e =1.654 x Iff' m' .s' (^ =0.2349), which is 
very close to the ambient value observed at z=40 m. The 
average circulation from both the port and starboard 
vortices is show in Fig. 6. The slightly faster decay for 
the starboard vortex may be due to the opposite sign 
vorticity of the ambient crosswind. Also included in Fig. 
6 for comparison, is measured Lidar data for the port 
vortex. The LES results and Lidar data show reasonable 
agreement with the circulation decay given by Eq. 1 . 

V. Ground Linking Experiments 

In the free atmosphere, the linking process begins as 
the counter-rotating circulations of a vortex pair connect, 
producing crude vortex rings. The time at which this 
linking takes place is a known function of the turbulence 



80 


/ (a). 


70 


f 


60 






I 50 






.1 '•0 
'^30 






20 






10 







% 



302 

e,(K) 




V (m/s) 



Figure 5. Initial profile of a) ambient potential 
temperature and b) crosswind for DFW, 26 September 
1997. 20:09 UTC. 



DALLAS 1997 IN GROUND EFFECT CASE 

97/09/26 2009:24 GMT 

Vortex 5-15 m Averaged Circulation Comparison 



n LidafObs Port (71=0 235) 

3D LES Port ln=0 233) 

-. 3D LES Star ln=0 233) 

^^^^ 0«caYMod«J 



.S200 - 



12 3 4 

Nondimensional TinDe (t b^„) 

Figure 6. Average circulation v.v nondimensional time 
for obser\'ed DFW case. Comparison of LES, Lidar, and 
IGE decay model (Eq. I ). 




American Institute of Aeronautics and Astronautics 



ETA = 0.3885 (T= 0.0 - 4.0) 
M TOP VIEW 



SIDE VIEW 




mMjkism^m^ijmi^ 



1.5 



2.5 



3.0 



3.5 







/-s 



•^ *^< 



■c/> 



1^ 



4.0 






f' 






Figure 7. Time evolution within IGE of wake vortex pair for r; = 0.388. Top (x.y) and. side (x.z) view of wake vortices 
at increments 0.5 nondimensional time units. 



American Instilute of Aeronautics and Astronautics 



ETA = 0.2333 (T= 0.0 - 4-.0) 
T M TOP VIEW 



SIDE VIEW 



ISO 

m 

»■ 

3.0 . 

-90 



'-^~* IJL- 




- 


•r. 


^_ 






-■ 




■*- 


"-■' ' 


• c 







St 


' . 1, 


^^ 


% fl 


*: *.-vJL>li^-r-i(kif! 


^ 


iO 


2» 


■> '/ « /.* . 


' 


V) 



^W*«V'**,^A«'V> 



>l f 



1S0- 
190- 






. 




:3.5 ": 

-so- 
-in- 

-1D0- 


--■ 










- 






4.5 



ISO 

IM 
90- 

5.0 0. 
-so 



5.5 



Figure 8. Same as Fig. 7, but for r) = 0.233. 



^^'^ 



■^V 



«■ 






30 


■^ 


% ' -» 


30' 




' 


10 







' <=,^- 



fl 1IU 21B 



10 
American Institute of Aeronautics and Astrxjnaulics 



Results from these simulations showed obvious 
ground linking to occur when ri exceeded 0..? (e.g. Fig 
7). For lower values of nondimensional turbulence 
intensity, pronounced vertical oscillations developed 
without obvious linking between the wake vortex and 
its ground image (e.g. Fig. 8). In none of the cases 
(which are all initiated well within IGE) did lateral 
linking occur. Influence of the very weak crosswind 
shear is unknown (see Fig. 5b), but ground linking only 
occurred with the port vortex. 

The visualization of the simulated wake vortex as 
it links with the ground is shown in Fig. 7. The port 
vortex becomes nearly vertical as it links with the 
ground just after T=2. For comparison, a photograph of 
an actual ground link is shown in Fig. 9. 




Figure 9. Observed case of ground linking (from 
NASA Langley photo archives, photograph L 90- 
02905) 

Both port and starboard vortices in Fig. 7 rapidly 
dissipate after linking, becoming undistinguishable 
fiom background turbulence at T=4. Note that in the 
vicinity of where the ground connection is to occur, the 
starboard vortex is transported upward and the port 
vortex downward. 



A ground linking factor can be defined similarly to 
Crow's linking parameter'* as: 

P(i)= ' 



+ Zn 



where ;„,„ and :„„„ are respectively, the maximum and 
minimum altitude of one of the vortices. Either the port 
or starboard vortex may be considered linked with its 
ground image when the linking factor exceeds 0.85. 
Table 6 shows nondimensional times for P to exceed 
both 0.7.5 and 0.85 as a function of nondimensional 
turbulence intensity. Also included is the linking time 
as predicted by Sarpkaya's" " " re-derivation of Crow 
and Bate's'" theoretical formula for vortex lifespan in 
the free atmosphere. In our experiments, ground 
linking did not occur for r| < 0.388. although the 
vertical linking parameter did grow with time. 
Additional experiments were carried out for larger 
domain sizes assuming ri =0.233, but little sensitivity 
was noted. Therefore, the linking time (or lack of 
linking) was not believed to be affected by our domain 
size. The influence of the crosswind shear on the 
suppression of linking for the lower turbulence levels is 
yet to be examined. 

Table 6. Sensitivity of Ground Linking to Ambient 
Turbulence (port vortex). 



Tb=0.75 TB=0.g5 Tsa 



0.233 


4.3 




2.4 


0.30 


2.90 




2.0 


0.388 


1.90 


2.10 


1.71 


0.50 


1.47 


1.63 


1.43 


0.75 


0.98 


1.14 


1.11 



Figure 10 shows a comparison of the tiine to 
ground link with experimental data" and theory'" '' for 
vortex linking in the free atmosphere. The three 
simulations that had ground linking are in close 
agreement with Sarpkaya's formula, even though 
the theory was developed for lateral vortex linking 
away from any ground influence. 



Figure 8 depicts the wake vortex system for a 
more moderate level of turbulence. Although an 
obvious link with the ground did not occur, a major 
portion of the port vortex remained parallel and very 
close to the ground. Again, note that the starboard 
vortex is at a relatively high altitude where the port 
vortex is closest to the ground. 



II 

American Institute of Aeronautics and Astronautics 



Vortex Lifespan (time to link or burst) 
vs Turbulence Intensity 



10' FT 



ho" 




EiqMrifmntal: Saipkaya 

TASS: OOE 
■ - Crow & Bate; Ttaonllcal 
— SirpkBY": Th«o(«tlcal 

TASS: Onund Link 



I I I I I inT^ I I I I I II 



10-' 10' 10" 

Normalized Turbulence Dissipation 



Figure 10. Linking time v.v nondimensitmal turbulence 
intensity. Time of ground linking from LES given by 
triangles, all other data for lateral linking (or vortex 
bursting) out of ground effect (OGE). 

VI. Summary and Conclusions 

A study of wake vortices initialized in-ground 
effect has been performed using a validated three- 
dimensional LES model. The simulations, which 
included environmental turbulence, show strong decay 
of wake vortices following maximum penetration into 
IGE. Wake vortex linking with its ground image was 
simulated for moderate to strong values of atmospheric 
turbulence. 

The primary conclusions of this study are: 

1 . Wake vortex transport and decay for IGE can 
be nondimensionalized with conventional 
parameters. 

2. Appropriate normalization of parameters 
reduces wake vortex sensitivity to initial 
circulation, initial separation, and generating 
height. 

3. Vortex decay for IGE has minor sensitivity to 
the ambient turbulence level. 

4. Based on the LES results, a formula for IGE 
decay is proposed. This formula, with few 
dependent parameters, should be easy to 
incorporate in wake vortex prediction models. 

5. Also based on the LES results, a model for 
lateral drift rate due to ground effect is 
proposed. 

6. Both the decay and drift models show very 
good agreement with the LES sensitivity 
results. 



Ground linking is influenced by the level of 
ambient turbulence. Similar to lateral linking 
in the free atmosphere, the time to ground link 
is a function of the nondimensional eddy 
dissipation. However, ground linking did not 
occur for moderate to weak levels of 
turbulence. 

The increased lateral separation of vortices 
from ground effect can suppress lateral vortex 
linking. 



Future work needs to address the sensitivity of 
crosswind shear to the onset vortex linking, both in and 
out of ground effect. 

Acknowledgements 

This research was sponsored by NASA's Terminal 
Area Productivity Program. One of the authors was 
funded under cooperative research grant NCCl-188. 
Numerical simulations were carried out on NASA and 
North Carolina Supercomputing Center 
supercomputers. 

Appendix - Sensitivity of Domain Size 

A number of experiments assume a truncated 
domain in the x-direction, so as to reduce compulation 
time, inhibit crow instability and simplify analysis of 
the experiments. The consequence of shortening the 
domain is evaluated here. Two simulations are carried 
out with everything identical except for a short domain: 
(L,, Ly. /,; = 2.2 b„. 10 b„. 2.2 b„), and a long domain 
(Z..,, Lv, Lz = '2.2 b„ 9.1 fc„, 2.2 bj. The ambient 
turbulence level is assumed as r\=0.2.U9 and each are 
resolved by the grid sizes listed in Table 3. The 
ambient temperature and crosswind are from profiles 
observed at 20. 09 UTC on 26 September 1997 at DFW 
(Fig. 5). 

Comparison of the average circulations from the 
two simulations with different domain sizes is shown in 
Fig. A- 1. Lidar observations from the L-1011 port 
vortex are also included. A comparison of lateral 
positions is shown in Fig. A-2. For this case, the 
figures indicate little sensitivity to domains size. 



12 
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(-00 (a) Port (n=0.2349) 



400 



300 



200 



I Lidar Obs, 
- L. = 2.2bo 
-- L, = 12.2bo 








20 



BO 



40 60 

Time (sec) 
Figure A-1. Time evolution of the 5-15 m averaged 
circulation for port vortex from short domain 
(Lx=2.2b„) and long domain (Lx=l2.2b„) simulations. 



100 



(a) Port (n=0.234 9) 



250- 



• Lidar Obs. 
— k = 2.2bo 
--- L,= 12.2bo 




Figure A-2. Same as Fig. A- 1, but for lateral position 
of port vortex. 



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American Institute of Aeronautics and Astronautics 



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